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15
On implementing the pushrelabel method for the maximum flow problem
, 1994
"... We study efficient implementations of the pushrelabel method for the maximum flow problem. The resulting codes are faster than the previous codes, and much faster on some problem families. The speedup is due to the combination of heuristics used in our implementation. We also exhibit a family of p ..."
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Cited by 151 (10 self)
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We study efficient implementations of the pushrelabel method for the maximum flow problem. The resulting codes are faster than the previous codes, and much faster on some problem families. The speedup is due to the combination of heuristics used in our implementation. We also exhibit a family of problems for which all known methods seem to have almost quadratic time growth rate.
An Efficient Implementation Of A Scaling MinimumCost Flow Algorithm
 Journal of Algorithms
, 1992
"... . The scaling pushrelabel method is an important theoretical development in the area of minimumcost flow algorithms. We study practical implementations of this method. We are especially interested in heuristics which improve reallife performance of the method. Our implementation works very well o ..."
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Cited by 99 (7 self)
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. The scaling pushrelabel method is an important theoretical development in the area of minimumcost flow algorithms. We study practical implementations of this method. We are especially interested in heuristics which improve reallife performance of the method. Our implementation works very well over a wide range of problem classes. In our experiments, it was always competitive with the established codes, and usually outperformed these codes by a wide margin. Some heuristics we develop may apply to other network algorithms. Our experimental work on the minimumcost flow problem motivated theoretical work on related problems. Supported in part by ONR Young Investigator Award N0001491J1855, NSF Presidential Young Investigator Grant CCR8858097 with matching funds from AT&T and DEC, Stanford University Office of Technology Licensing, and a grant form the Powell Foundation. 1 1. Introduction. Significant theoretical progress has been made recently in the area of minimumcost flow ...
Graph clustering and minimum cut trees
 Internet Mathematics
, 2004
"... Abstract. In this paper, we introduce simple graph clustering methods based on minimum cuts within the graph. The clustering methods are general enough to apply to any kind of graph but are well suited for graphs where the link structure implies a notion of reference, similarity, or endorsement, suc ..."
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Cited by 53 (3 self)
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Abstract. In this paper, we introduce simple graph clustering methods based on minimum cuts within the graph. The clustering methods are general enough to apply to any kind of graph but are well suited for graphs where the link structure implies a notion of reference, similarity, or endorsement, such as web and citation graphs. We show that the quality of the produced clusters is bounded by strong minimum cut and expansion criteria. We also develop a framework for hierarchical clustering and present applications to realworld data. We conclude that the clustering algorithms satisfy strong theoretical criteria and perform well in practice. 1.
Experimental Study of Minimum Cut Algorithms
 PROCEEDINGS OF THE EIGHTH ANNUAL ACMSIAM SYMPOSIUM ON DISCRETE ALGORITHMS (SODA)
, 1997
"... Recently, several new algorithms have been developed for the minimum cut problem. These algorithms are very different from the earlier ones and from each other and substantially improve worstcase time bounds for the problem. We conduct experimental evaluation the relative performance of these algor ..."
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Cited by 40 (2 self)
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Recently, several new algorithms have been developed for the minimum cut problem. These algorithms are very different from the earlier ones and from each other and substantially improve worstcase time bounds for the problem. We conduct experimental evaluation the relative performance of these algorithms. In the process, we develop heuristics and data structures that substantially improve practical performance of the algorithms. We also develop problem families for testing minimum cut algorithms. Our work leads to a better understanding of practical performance of the minimum cut algorithms and produces very efficient codes for the problem.
An Efficient Cost Scaling Algorithm for the Assignment Problem
 MATH. PROGRAM
, 1995
"... The cost scaling pushrelabel method has been shown to be efficient for solving minimumcost flow problems. In this paper we apply the method to the assignment problem and investigate implementations of the method that take advantage of assignment's special structure. The results show that the metho ..."
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Cited by 38 (1 self)
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The cost scaling pushrelabel method has been shown to be efficient for solving minimumcost flow problems. In this paper we apply the method to the assignment problem and investigate implementations of the method that take advantage of assignment's special structure. The results show that the method is very promising for practical use.
Augment or Push? A computational study of Bipartite Matching and Unit Capacity Flow Algorithms
 ACM J. EXP. ALGORITHMICS
, 1998
"... We conduct a computational study of unit capacity flow and bipartite matching algorithms. Our goal is to determine which variant of the pushrelabel method is most efficient in practice and to compare pushrelabel algorithms with augmenting path algorithms. We have implemented and compared three pus ..."
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Cited by 30 (1 self)
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We conduct a computational study of unit capacity flow and bipartite matching algorithms. Our goal is to determine which variant of the pushrelabel method is most efficient in practice and to compare pushrelabel algorithms with augmenting path algorithms. We have implemented and compared three pushrelabel algorithms, three augmenting path algorithms (one of which is new), and one augmentrelabel algorithm. The depthfirst search augmenting path algorithm was thought to be a good choice for the bipartite matching problem, but our study shows that it is not robust. For the problems we study, our implementations of the fifo and lowestlevel selection pushrelabel algorithms have the most robust asymptotic rate of growth and work best overall. Augmenting path algorithms, although not as robust, on some problem classes are faster by a moderate constant factor. Our study includes several new problem families and input graphs with as many as 5 \Theta 10 5 vertices.
Recent Developments in Maximum Flow Algorithms
 in Proceedings of Scandinavian Workshop on Algorithm Theory (SWAT
, 1998
"... Introduction The maximum flow problem is a classical optimization problem with many applications; see e.g. [1, 18, 39]. Algorithms for this problem have been studied for over four decades. Recently, significant improvements have been made in theoretical performance of maximum flow algorithms. In t ..."
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Cited by 23 (1 self)
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Introduction The maximum flow problem is a classical optimization problem with many applications; see e.g. [1, 18, 39]. Algorithms for this problem have been studied for over four decades. Recently, significant improvements have been made in theoretical performance of maximum flow algorithms. In this survey we put these results in perspective and provide pointers to the literature. We assume that the reader is familiar with basic flow algorithms, including Dinitz' blocking flow algorithm [13]. 2 Preliminaries The maximum flow problem is to find a flow of the maximum value given a graph G with arc capacities, a source s, and a sink t, Here a flow is a function on arcs that satisfies capacity constraints for all arcs and conservation constraints for all vertices except the source and the sink. For more details, see [1, 18, 39]. We distinguish between directed
Global price updates help
, 1997
"... Periodic global updates of dual variables have been shown to yield a substantial speed advantage in implementations of pushrelabel algorithms for the maximum flow and minimum cost flow problems. In this paper, we show that in the context of the bipartite matching and assignment problems, global upd ..."
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Cited by 11 (4 self)
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Periodic global updates of dual variables have been shown to yield a substantial speed advantage in implementations of pushrelabel algorithms for the maximum flow and minimum cost flow problems. In this paper, we show that in the context of the bipartite matching and assignment problems, global updates yield a theoretical improvement as well. For bipartite matching, a pushrelabel algorithm that uses global updates runs in O ( √ log(n nm 2) /m) time (matching the best bound log n known) and performs worse by a factor of √ n without the updates. A similar result holds for the assignment problem, for which an algorithm that assumes integer costs in the range [ −C,...,C] and that runs in time O ( √ nm log(nC)) (matching the best costscaling bound known) is presented.
Length Functions for Flow Computations
 NEC Research Institute
, 1997
"... We introduce a new approach to the maximum flow problem. This approach is based on assigning arc lengths based on the residual flow value and the residual arc capacities. Our approach leads to an O(min(n 2=3 ; m 1=2 )m log( n 2 m ) log U) time bound for a network with n vertices, m arcs, and ..."
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Cited by 10 (0 self)
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We introduce a new approach to the maximum flow problem. This approach is based on assigning arc lengths based on the residual flow value and the residual arc capacities. Our approach leads to an O(min(n 2=3 ; m 1=2 )m log( n 2 m ) log U) time bound for a network with n vertices, m arcs, and integral arc capacities in the range [1; : : : ; U ]. This is a fundamental improvement over the previous time bounds. We also improve bounds for the GomoryHu tree problem, the parametric flow problem, and the approximate st cut problems. 1 Introduction The maximum flow problem and its dual, the minimum cut problem, are classical combinatorial problems with a wide variety of scientific and engineering applications. The maximum flow problem and related flow and cut problems have been studied intensively for over three decades. The network simplex method of Dantzig [11] for the transportation problem, published in 1951, solves the maximum flow problem as a natural special case. Soon ther...
Performance analysis and best implementations of old and new algorithms for the OpenPit Mining Problem
 Operations Research
, 1998
"... The openpit mining problem is to determine the contours of a mine, based on economic data and engineering feasibility requirements in order to yield maximumpossible net income. This practical problem needs to be solved for very large data sets. In practice, moreover, it is necessary to test mult ..."
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Cited by 7 (1 self)
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The openpit mining problem is to determine the contours of a mine, based on economic data and engineering feasibility requirements in order to yield maximumpossible net income. This practical problem needs to be solved for very large data sets. In practice, moreover, it is necessary to test multiple scenarios taking into account a variety of realizations of geological predictions and forecasts of ore value. The industry is experiencing computational difficulties in solving the problem. Yet, the problem is known to be equivalent to the minimum cut or maximum flow problem. For the maximum flow problem there are a number of very efficient algorithms that have been developed over the last decade. On the other hand, the algorithm that is most commonly used by the mining industry has been devised by Lerchs and Grossmann (LG) [LG64]. This algorithm is used in most commercial software packages for openpit mining. This paper describes a detailed study of the LG algorithm as compare...